Method for suppression of ofdm energy spectral density for minimization of out of band emission or utilization of fractured spectrum

ABSTRACT

The Energy spectral density of OFDM signals inherently rolls off slowly. Slow OFDM spectral rolloff has system level implications traditionally mitigated by some combination of the following: addition of bandlimiting filtering; use of significant guard bands of zeroed tones; and, guard time shaping. Each of these techniques negatively impact system performance and/or flexibility. This application presents a methodology for active cancellation of out of band spectral energy. The technique can be used by itself or in conjunction with above traditional methods to help control out of band emission. Examples of the use of the new technique are provided. Computational cost of the new technique is also discussed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. Utility application Ser. No.11/824,723, filed on Jul. 2, 2007, which claims the benefit under 35U.S.C Section 119(e) of U.S. Provisional Application Ser. No.60/818,558, filed on Jul. 5, 2006, by Robert F. Popoli and John L.Norin, entitled “METHOD FOR SUPPRESSION OF OFDM ENERGY SPECTRAL DENSITYFOR MINIMIZATION OF OUT-OF-BAND EMISSION OR UTILIZATION OF FRACTUREDSPECTRUM,” which applications are incorporated by reference herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to wireless data systems, and inparticular, to a method, apparatus, and article of manufacture forsuppressing OFDM energy spectral density to minimize out-of-bandemissions.

2. Description of the Related Art

Orthogonal Frequency Division Multiplexed (OFDM) signals are comprisedof a set of subcarriers (also referred to as tones) which areconstructed such that they are orthogonal to each other even though theyoverlap significantly in frequency. This is achieved as follows.

As far as the matched filter in the receiver is concerned (nuance hereis that a cyclical prefix is added prior to transmission but removedprior to matched filter reception), each subcarrier, sk(t), during asymbol period, T, is a sinusoid of the form

${s_{k}(t)} = \left\{ \begin{matrix}{\sin \left( {\omega_{o}k\; t} \right)} & {0 < t < T} \\0 & {otherwise}\end{matrix} \right.$

It is easy to establish the orthogonality of such symbols by verifying

${\int_{0}^{T}{{s_{i}(t)}{s_{j}(t)}\ {t}}} = \left\{ \begin{matrix}C & {i = j} \\0 & {i \neq j}\end{matrix} \right.$

In the time domain, the symbols are equal to a sinusoid times arectangular time window of length T. Therefore in the frequency domain,the energy spectral density of each symbol is the convolution of a diracdelta function .(!.!o) with a Sinc( ) function, T Sinc(ƒT) (which hasnulls at ƒ=k=T 8k=0.1; 0.2; : : : ). If the subcarrier spacing ƒo is setat

$f_{o} = {\frac{\omega_{o}}{2\; \pi} = {1/T}}$

then each subcarrier sits at the null of all other subcarriers. This isanother way to recognize the orthogonality of the OFDM subcarriers.Thus, the baseband energy spectral density of the OFDM subcarrier sk(t)is given by

S(ƒ)=A _(i) _(k) Sin c(ƒ−kƒ _(o))

where A_(ik) is the ith complex symbol which modulates the kthsubcarrier during the ith symbol period. The composite OFDM energyspectral density of the ith symbol of all subcarriers is then just

$\sum\limits_{k}\; {A_{i_{k}}{Sin}\; {c\left( {f - {k\; f_{o}}} \right)}}$

The relevance of this is that the Sinc function falls off very slowlywith frequency. Since each of the subcarriers falls off slowly withfrequency so does the aggregate OFDM signal as can been seen in FIG. 1A.

FIG. 1A shows a typical energy spectral density sample 100 from a 512tone QPSK modulated OFDM signal. FIG. 1A shows the characteristic slowroll off. There are several methods employed to help mitigate this slowroll off. One of the primary techniques is to specify that a certainnumber, NGuard, of tones at the edge of the band are to be dedicated“guard” tones which are in fact not energized.

FIG. 1B depicts this technique as it is specified in the 802.16specification. The 802.16 common air interface calls for a number oftones to be unused at the edges (and a “zeroed” DC tone as well). Theexact number of tones specified to be “zeroed” is a function of the FFTorder (i.e. the number of tones) and other system parameters.

FIG. 1B depicts graph 100 in comparison with graph 102, where graph 102uses a typical 512 tone scenario where 40 left hand tones areun-energized and 39 right hand tones are un-energized (i.e., NGuard=79).Marked on FIGS. 1A and 1B are point 104 are tones 255 where the upperend of the OFDM spectrum stops if no guard tones are used and point 106,at tone 216, where the upper end of the OFDM spectrum stops if guardtones are used. FIG. 1B shows via graph 102 what happens to the energyspectral density of the upper band edge when the guard tones aredeployed. In essence, the energy spectral density is decreased when theactive cancellation of the present invention is used.

If an adjacent system would like to deploy close to this OFDM signal,the use of the guard tones drops the Out Of Band (OOB) emission byapproximately 30 dB at band edge (i.e., at tone 256). It can also beseen from FIG. 1B that since the spectrum falls off rather slowly fromthe point 255 on, adding more guard tones would only provide modestfurther improvement. It is important to note the expense of these guardtones. The guard tones represent 79/512 of the spectrum or 15.4%. Thus,the use of guard tones represents 15.4% wasted bandwidth.

Perhaps one of the most typical approaches to controlling OOB roll offis to simply bandpass filter the composite OFDM signal. This is done inmost systems which need more roll off than that which is provided by theutilization of guard tones. Bandpass filtering has two significantdisadvantages beyond the mere fact that it adds hardware (HW)complexity. The first disadvantage occurs when significant edge of bandroll off is required. First, note that the spectral occupancy of an OFDMtone is actually quite large (recall from Eq. (5) that significant toneenergy extends over many tone intervals). Due to the large spectralextent, a brick wall filter will cut off a significant amount of theenergy of the outer edge tones and thus directly reduce the Signal toNoise Ratio (SNR) of the output of the matched filter receiver for thesetones. This then affects the Bit Error Rate (BER) performance of theouter tones. Furthermore, a brick wall filter may have significantdifferential group delay which will affect the orthogonality of theouter tones relative to the rest of the OFDM set. This can affect the(SNR) of the inner tones since the edge tones will contribute to theirInter-Carrier Interference (ICI). Thus the BER performance of the innertones will suffer.

In the case of a large scale deployment, the use of bandpass filters haspotentially an even greater cost. In a large scale deployment, theavailable spectrum can change slightly with time and with location dueto regulatory changes or spectrum negotiations. HW bandpass filters canmake it very expensive to adjust for changes in available spectrum. Thislack of flexibility can have enormous financial impact. On thesubscriber equipment side, the issue is somewhat less severe since theseunits tend not to be the main source of inter system interference (theytransmit at lower power and have less line of sight because subscriberequipment is not tower mounted). Furthermore, subscriber equipment canbe dynamically directed to not use frequencies near band edge. Finally,subscriber HW can be constructed based on a narrower tunable BW, unlikea base station which must transmit simultaneously over the entireavailable BW. The above discussion has bearing on the application of thenew technique of the present invention. Employing the proposed techniqueonly on the base stations (where it is most practical) may besufficient. Finally, another technique which can be used to shape theOOB spectrum is to provide a temporal shaping of the guard time. InOFDM, the symbols are temporally extended through the use of a cyclicalprefix. This prefix is used to help mitigate multipath effects and isremoved by the receiver prior to matched filtering. The 802.11specification recommends such shaping as a potential approach but doesnot insist upon its use if OOB spectral masks can be met without it. The802.16 specification does not suggest cyclical prefix shaping. The costof this technique is added HW/computational complexity.

Furthermore, some studies suggest that to get enough benefit from theguard time shaping the cyclical prefix would need to be extended beyondthat which is required for multipath mitigation to allow for moregradual rise times. Such extension would directly impact system capacitysince it reduces symbol rate without increasing SNR.

No mention of the contribution of spectral regrowth due to High PowerAmplifier (HPA) nonlinearities herein. OFDM tends to have a relativelylarge Crest Factor (CF). This requires the power amplifiers used forOFDM applications to be operated with an Output Back Off (OBO) on theorder of 10 dB. Note that guard tones will help contain spectralregrowth somewhat by narrowing the transmitted spectrum. In contrast,note that bandpass filtering generally must be done prior to the HPA.Therefore, bandpass filtering will not be very helpful if HPA inducedspectral regrowth of the bandlimited signal produces unacceptable OBO.Guard time shaping will similarly not help if spectral regrowthdominates.

Spectral regrowth due to HPA nonlinearities must be primarily mitigatedthrough some combination of sufficient output backoff and CF managementthrough data and or guard tone manipulation. More exotically non-linearpre-distortion can be attempted.

SUMMARY OF THE INVENTION

To minimize the limitations in the prior art, and to minimize otherlimitations that will become apparent upon reading and understanding thepresent specification, the present invention discloses methods forsuppressing Orthogonal Frequency Division Multiplexing (OFDM) energyspectral density. A method in accordance with the present inventioncomprises transmitting data tones and at least one guard tone in afrequency band, and energizing the at least one guard tone wherein anextended spectral energy side lobe of the at least one guard tonecancels at least one extended spectral energy side lobe of the pluralityof data tones in a specified region of the frequency band.

Such a method further optionally comprises the specified region of thefrequency band being adjacent to a band edge of the frequency band, aplurality of guard tones are energized, the plurality of guard tones areselected based on a characteristic of the selected guard tones, and thecharacteristic is an orthogonality of the selected guard tones.

Another method in accordance with the present invention comprisesselecting a set of cancellation tones to be used for energy spectraldensity cancellation, constructing a set of orthonormal basis vectors inat least one frequency region where the OFDM energy spectral density isto be cancelled based on the selected set of cancellation tones,computing a projection of a unity magnitude data modulated tone at eachcancellation tone frequency onto the respective orthonormal basisvectors, employing a set of data excitations to scale the unitymagnitude projections to find a projection of a side lobe of symbol dataonto the set of orthonormal basis vectors, and applying the projectionof the side lobe of symbol data to set an amplitude and a phase of eachof the cancellation tones.

Such a method further optionally includes the set of cancellation tonesare selected from a guard band of frequencies, at least one of the tonesin the set of cancellation tones is selected from the guard band offrequencies, a frequency spectrum in the OFDM energy spectral densitycomprises a stay out zone, tones in the set of cancellation tones areselected from a first guard band and a second guard band, the firstguard band is in a frequency spectrum immediately below the OFDM databand and the second guard band is in a frequency spectrum immediatelyabove the OFDM data band, and the set of cancellation tones consists ofeither eight or fourteen cancellation tones.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawings in which like reference numbers representcorresponding parts throughout:

FIG. 1A illustrates an inherent energy spectral density of OFDM with noout-of-band suppression techniques applied; FIG. 1B illustrates a BandEdge comparison with and without guard tone utilization;

FIGS. 2A and 2B illustrate eight orthogonal basis vectors designed forcancellation in specific regions of the spectrum;

FIG. 3 shows a close up of the eight orthogonal basis vectors in part ofthe upper region of the spectrum;

FIG. 4 illustrates an energy spectral density prior to activecancellation;

FIG. 5 shows the energy spectral density after active cancellation;

FIG. 6 shows a close up of upper cancellation region results;

FIG. 7 illustrates a close up of the lower cancellation region results;

FIG. 8 illustrates an energy spectral density graph prior to activecancellation;

FIG. 9 illustrates fourteen orthogonal basis vectors designed forcancellation in three depicted regions;

FIG. 10 shows the energy spectral density after active cancellation;

FIG. 11 shows a close up of cancellation region 1 results;

FIG. 12 shows a close up of cancellation region 2 results;

FIG. 13 shows a close up of cancellation region 3 results; and

FIGS. 14 and 15 illustrate preferred processes in accordance with thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the following description, reference is made to the accompanyingdrawings which form a part hereof, and which is shown, by way ofillustration, several embodiments of the present invention. It isunderstood that other embodiments may be utilized and structural changesmay be made without departing from the scope of the present invention.

Overview

The present invention uses active cancellation through the guard tonesto cancel the extended spectral energy side lobes of the data tones indesired regions. The technique of the present invention mitigates OOBwhich can be used in conjunction with or instead of the abovetraditional techniques. The present invention energize some of the guardtones in such a way that their extended spectral energy side lobescancel the extended spectral energy side lobes of the data tones inspecified regions (generally regions adjacent to band edge).

The goal of the present invention is to do this in a way that is notexcessively computationally burdensome. To this end, the goal is to tryto structure the algorithm in such a way that the majority of thecomputational burden need not be done in real time. When used inconjunction with other techniques, the proposed technique has theadvantage of achieving more OOB rolloff than would be practical toachieve with the traditional techniques alone. This additional OOBrolloff could increase the utility of spectrum which is otherwise tooclose to other already occupied spectrum or for which very strictregulatory masks have been established. When used as an alternate tofixed HW band pass filtering, the technique has the significantadvantage that it allows for software adaptation to slight changes inspectrum availability which might occur due to regulatory changes orfuture spectrum negotiations. For a wide scale deployment this factorcould have financial significance.

Active OOB Cancellation

In order to provide a context for the detailed description of theproposed method, a brief summary of the approach is first presented. Inoutline form, the approach is:

-   1) Select a set of tones to be used for energy spectral density    cancellation.-   2) From the tones selected in Step 1, construct a set of orthonormal    basis vectors in the frequency regions where the OOB energy    cancellation is desired.-   3) Compute the projection of a unity magnitude data modulated tone    at each tone frequency k!o onto the orthonormal basis vectors found    in Step 2.-   4) For each ith symbol period, employ the set of data excitations    Aik 8k to scale the unity magnitude projections found in step 3 to    find the projection of the side lobes of the ith symbol's data onto    the orthonormal basis set.-   5) Use the results of Step 4 to set the amplitude and phase of each    of the cancellation tones.

The degree of cancellation achieved will be the degree to which theselected cancellation tones span the space of the side lobes of the datatones in the area in which cancellation is being attempted. Somecomments on the computation are in order. First, note that Step 1through Step 3 can be pre-computed. When the algorithm details arepresented, it will be shown that a significant portion of thecomputation of Step 4 can also be pre-computed.

Finally, once the data cancellation tones have been pre-selected, theentire algorithm is deterministic. No optimization search is required inreal time. Thus the real time computational burden is completely knownand constant during the real time operation.

The details of the algorithm are as follows. Assume the set of Ngcancellation tones

$g_{i} = {{{Sin}\; {c\left( \frac{f - {k\; f_{o}}}{2\; \pi} \right)}\mspace{14mu} {is}\mspace{14mu} {given}\mspace{14mu} {by}\mspace{14mu} {the}\mspace{14mu} {set}\mspace{14mu} {G.G}} = \left\{ {g_{i}:{i \in {1\mspace{14mu} \ldots \mspace{14mu} N_{g}}}} \right\}}$

Further, assume there are N_(r) regions R in which energy spectraldensity suppression is desired and that these regions are given by

R={{ω, R _(low) _(i) , R _(hi) _(i) }:i∈1 . . . N _(R)}

where the tuple indicates a region of frequency extending from ω=R_(low)to ω=R_(hi) in which spectral cancellation is attempted.

Orthonormal basis vectors are then established by iteratively computinga Gram Schmidt Orthogonalization. The first basis is computed as

$\Psi_{1} = {\frac{g_{1}}{\sqrt{{< g_{1}},{g_{1} >_{R}}}} = \frac{g_{1}}{{g_{1}}_{R}}}$

and in general the nth basis is calculated as

$\Psi_{n} = \frac{{{g_{n} - \sum\limits_{i = 1}^{n - 1}}\; < g_{n}},{\Psi_{i} >_{R}\Psi_{i}}}{{{{g_{n} - {\sum\limits_{i = 1}^{n - 1}\; {< g_{n}}}},{\Psi_{i} >_{R}\Psi_{i}}}}_{R}}$

Proceeding in this fashion, an orthonormal basis can be constructed.Each orthonormal basis ψ_(n) is thus defined as a mixture of the g_(i)tones. These equations can be arranged in a matrix equation as

$\Psi = {{{Cg}\begin{pmatrix}\Psi_{1} \\\Psi_{2} \\\vdots \\\Psi_{N_{g}}\end{pmatrix}} = {\begin{pmatrix}c_{11} & 0 & \ldots & 0 \\c_{21} & c_{22} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\c_{N_{g}1} & c_{N_{g}2} & \ldots & c_{N_{g}N_{g}}\end{pmatrix}\begin{pmatrix}g_{1} \\g_{2} \\\vdots \\g_{N_{g}}\end{pmatrix}}}$

Next, the inner product of unity scaled data tones sk (i.e. data toneswith A_(ik)=1) with each of the basis vectors is pre-computed andarranged in a matrix B.

$= \begin{pmatrix}{{< s_{k_{\min}}},{\Psi_{1} >_{R}}} & {{< s_{k_{\min}}},{\Psi_{2} >_{R}}} & \ldots & {{< s_{k_{\min}}},{\Psi_{N_{g}} >_{R}}} \\{{< s_{k_{\min} + 1}},{\Psi_{1} >_{R}}} & {{< s_{k_{\min} + 1}},{\Psi_{2} >_{R}}} & \ldots & {{< s_{k_{\min} + 1}},{\Psi_{N_{g}} >_{R}}} \\\vdots & \vdots & \ddots & \vdots \\{{< s_{k_{\max}}},{\Psi_{1} >_{R}}} & {{< s_{k_{\max}}},{\Psi_{2} >_{R}}} & \ldots & {{< s_{k_{\max}}},{\Psi_{N_{g}} >_{R}}}\end{pmatrix}$

With these quantities in place, cancellation is achieved as described insteps 4 and 5 of the outlined procedure as follows. Form the toneexcitation vector Ai for the ith data symbol as

A_(i) = (A_(i_(k_(min)))A_(i_(k_(min) + 1))  …  A_(i_(k_(max))))

The projection of the data onto the basis vectors is then given by AiB.

The projection of this resultant on to the cancellation tone vector gyields the complex weights wi that need to be applied to thecancellation tones to achieve the active cancellation of the side lobeenergy spectral density of the ith symbol. These weights are thus givenby

ω_(i) =A _(i)

Only Ai is not known in advance. Therefore, the calculation BC can beperformed in advance to yield a static compensation matrix H. Thus, theonly real time operation which is required is the multiplication of thecomplex modulation weights Ai of the ith symbol by the staticpre-computed compensation matrix H. This yields the desired complexcancellation tone weights wi for cancellation of the energy spectraldensity of the ith symbol set in the specified regions R. Thus

ω_(i) =A _(i)

The computational burden of the algorithm is as follows. Ai hasdimensions 1. (NFFT.NGuard). For example, in the present case, Ai hasdimension 1. (512.79)=1.433. The corresponding H has dimensions 433. Ng.In the next example, good results can be achieved with Ng (number ofcompensation tones) equal 8. Thus, the real time computational burden isthe burden of the matrix multiply AiH. Thus, for this example, theburden is 1.433.8=3464 mac (mac=MultiplyAccumulate).

As a point of comparison, the normal implementation of OFDM uses an IFFTto generate the tones for transmission. Thus, for the 512 tone case, thecomputational burden to produce the data for transmission is thecomputational burden to perform a NFFT point IFFT. The Fast FourierTransform has a computational burden of NLog2(N). Thus, thecomputational burden of the OFDM generation is 512.9=4608 mac. Bycomparison, the active cancellation requires 3464 mac. Although thecomputational burden is not cheap, it is not unreasonable. Further, fora NFFT=1024 the normal OFDM computation burden rises a little fasterthan linearly to 10240 mac while the burden of active cancellation riseslinearly to 6928 (assuming the same guard ratio and same number ofcancellation tones).

Sample Results—Case 1

The first case is the active cancellation of the regions just outsidethe passband. The 512 tone QPSK modulated OFDM signal with 79 guardtones as shown in FIG. 1B is the starting point. Eight of these guardtones were selected for active cancellation of the energy spectraldensity in two regions just outside the passband. The lower regionstarts at the last active tone at −257 and extends out to the equivalentof tone −500. The upper cancellation region starts at the last activetone at 256 and extends to the equivalent of tone 500. The 8 guard toneswhich are energized to achieve cancellation are {256, 0.241, 0.226,0.211, 210, 225, 240, 255}.

FIGS. 2A-2B shows the set of 8 orthogonal basis vectors that wereformed. FIG. 2A illustrates the eight vectors 200 that were used in thelower cancellation region and FIG. 2B illustrates the eight vectors 202that were used in the upper cancellation region. FIG. 3 shows a close upof the base vectors in a portion of the upper region.

FIG. 4 illustrates a typical energy spectral density, similar to thatshown in FIG. 1A, as graph 100. FIG. 5 shows the energy spectral densityafter cancellation, with graph 100 and graph 102 shown for comparison.FIG. 6 shows a close up of the upper cancellation portion, which showsapproximately 30-40 dB of cancellation for the energy spectral densityacross the spectrum. FIG. 7 illustrates the lower cancellation region,which achieved similar results as those shown for the upper cancellationregion in FIG. 6.

Sample Results—Case 2

The next case is an extension of the first. The setup is similar exceptthat a third cancellation region was added which extended from tone 30to tone 50. This allowed for the case where the available spectrum isfractured into two by an intervening stay out zone (from tone 30 to 50).The goal was to see how much cancellation could be achieved across thethree zones. Guard tones were added on either side of the stay out zonesuch that tones 0 through 80 were not used for data. Additionalenergized tones were added to the 8 used in Case 1. The new energizedcancellation tones for this case were {1, 14, 29, 52, 67, 82}.

FIG. 8 shows the pre-compensated input 800 with stay-out zone 802. FIG.9 illustrates shows the 14 developed orthogonal cancellation signals,lower cancellation zone signals 900, upper cancellation zone signals902, and stay-out zone cancellation signals 904, with tone number on thex axis.

FIG. 10 illustrates the cancellation effects in graph 1000 as comparedto input 800. FIG. 11 shows the lower cancellation region in moredetail, again with graph 1000 compared to input 800. FIG. 12 shows theupper cancellation region in more detail, again with graph 1000 comparedto input 800. FIG. 13 shows the stay-out zone cancellation region inmore detail, again with graph 1000 compared to input 800. It maytherefore be useful to combine the technique of the present inventionwith CF management or waveform predistortion.

Process Chart

FIG. 14 illustrates a preferred process in accordance with the presentinvention.

Box 1400 illustrates transmitting data tones and at least one guard tonein a frequency band.

Box 1402 illustrates energizing the at least one guard tone wherein anextended spectral energy side lobe of the at least one guard tonecancels at least one extended spectral energy side lobe of the pluralityof data tones in a specified region of the frequency band.

FIG. 15 illustrates another preferred process in accordance with thepresent invention.

Box 1500 illustrates selecting a set of cancellation tones to be usedfor energy spectral density cancellation.

Box 1502 illustrates constructing a set of orthonormal basis vectors inat least one frequency region where the OFDM energy spectral density isto be cancelled based on the selected set of cancellation tones.

Box 1504 illustrates computing a projection of a unity magnitude datamodulated tone at each cancellation tone frequency onto the respectiveorthonormal basis vectors.

Box 1506 illustrates employing a set of data excitations to scale theunity magnitude projections to find a projection of a side lobe ofsymbol data onto the set of orthonormal basis vectors.

Box 1508 illustrates applying the projection of the side lobe of symboldata to set an amplitude and a phase of each of the cancellation tones.

CONCLUSION

The present invention comprises methods for suppressing OrthogonalFrequency Division Multiplexing (OFDM) energy spectral density. A methodin accordance with the present invention comprises transmitting datatones and at least one guard tone in a frequency band, and energizingthe at least one guard tone wherein an extended spectral energy sidelobe of the at least one guard tone cancels at least one extendedspectral energy side lobe of the plurality of data tones in a specifiedregion of the frequency band.

Such a method further optionally comprises the specified region of thefrequency band being adjacent to a band edge of the frequency band, aplurality of guard tones are energized, the plurality of guard tones areselected based on a characteristic of the selected guard tones, and thecharacteristic is an orthogonality of the selected guard tones.

Another method in accordance with the present invention comprisesselecting a set of cancellation tones to be used for energy spectraldensity cancellation, constructing a set of orthonormal basis vectors inat least one frequency region where the OFDM energy spectral density isto be cancelled based on the selected set of cancellation tones,computing a projection of a unity magnitude data modulated tone at eachcancellation tone frequency onto the respective orthonormal basisvectors, employing a set of data excitations to scale the unitymagnitude projections to find a projection of a side lobe of symbol dataonto the set of orthonormal basis vectors, and applying the projectionof the side lobe of symbol data to set an amplitude and a phase of eachof the cancellation tones.

Such a method further optionally includes the set of cancellation tonesare selected from a guard band of frequencies, at least one of the tonesin the set of cancellation tones is selected from the guard band offrequencies, a frequency spectrum in the OFDM energy spectral densitycomprises a stay out zone, tones in the set of cancellation tones areselected from a first guard band and a second guard band, the firstguard band is in a frequency spectrum immediately below the OFDM databand and the second guard band is in a frequency spectrum immediatelyabove the OFDM data band, and the set of cancellation tones consists ofeither eight or fourteen cancellation tones.

The foregoing description of the preferred embodiment of the inventionhas been presented for the purposes of illustration and description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed. Many modifications and variations are possiblein light of the above teaching. It is intended that the scope of theinvention be limited not by this detailed description, but by the claimsappended hereto and the full range of equivalents of the claims appendedhereto.

1. A method for suppressing Orthogonal Frequency Division Multiplexing(OFDM) energy spectral density for a plurality of data tones in afrequency band, comprising: constructing a set of orthonormal basisvectors in at least one frequency region where the OFDM energy spectraldensity is to be cancelled; setting an amplitude and phase of a guardtone based on the orthonormal basis vectors; and energizing the guardtone wherein an extended spectral energy side lobe of the guard tonecancels at least one extended spectral energy side lobe of the pluralityof data tones.
 2. The method of claim 1, wherein the plurality of datatones are adjacent to a band edge of the frequency band.
 3. The methodof claim 1, wherein a plurality of guard tones are energized.
 4. Themethod of claim 3, wherein the plurality of guard tones are selectedbased on an orthogonality of the selected guard tones.
 5. A method forcanceling Orthogonal Frequency Division Multiplexing (OFDM) energyspectral density, comprising: constructing a set of orthonormal basisvectors in at least one frequency region where the OFDM energy spectraldensity is to be cancelled based on a selected set of cancellationtones; computing a projection of a unity magnitude data modulated toneat each cancellation tone frequency onto the respective orthonormalbasis vectors; scaling the unity magnitude projections to find aprojection of a side lobe of symbol data onto the set of orthonormalbasis vectors; and applying the projection of the side lobe of symboldata to set an amplitude and a phase of each of the cancellation tones.6. The method of claim 5, wherein the set of cancellation tones areselected from a guard band of frequencies.
 7. The method of claim 5,wherein at least one of the tones in the set of cancellation tones isselected from a guard band of frequencies.
 8. The method of claim 7,wherein a frequency spectrum in the OFDM energy spectral densitycomprises a stay out zone.
 9. The method of claim 8, wherein tones inthe set of cancellation tones are selected from a first guard band and asecond guard band.
 10. The method of claim 9, wherein the first guardband is in a frequency spectrum immediately below the OFDM data band andthe second guard band is in a frequency spectrum immediately above theOFDM data band.
 11. The method of claim 10, wherein the set ofcancellation tones consists of fourteen cancellation tones.
 12. Themethod of claim 6, wherein tones in the set of cancellation tones areselected from a first guard band and a second guard band.
 13. The methodof claim 12, wherein the first guard band is in a frequency spectrumimmediately below the OFDM data band and the second guard band is in afrequency spectrum immediately above the OFDM data band.
 14. The methodof claim 13, wherein the set of cancellation tones consists of eightcancellation tones.
 15. A method for canceling Orthogonal FrequencyDivision Multiplexing (OFDM) energy spectral density, comprising:constructing a set of orthonormal basis vectors based on a selected setof cancellation tones; computing a projection of a unity magnitude datamodulated tone at each cancellation tone frequency onto the respectiveorthonormal basis vectors; finding, from the projection of the unitymagnitude data modulated tone, a projection of a side lobe of symboldata onto the set of orthonormal basis vectors; and applying theprojection of the side lobe of symbol data to set an amplitude and aphase of each of the cancellation tones.
 16. The method of claim 15,wherein the set of cancellation tones are selected from a guard band offrequencies.
 17. The method of claim 15, wherein at least one of thetones in the set of cancellation tones is selected from a guard band offrequencies.
 18. The method of claim 17, wherein a frequency spectrum inthe OFDM energy spectral density comprises a stay out zone.
 19. Themethod of claim 18, wherein tones in the set of cancellation tones areselected from a first guard band and a second guard band.
 20. The methodof claim 19, wherein the first guard band is in a frequency spectrumimmediately below the OFDM data band and the second guard band is in afrequency spectrum immediately above the OFDM data band.